Einstein and Specific Heats
The more success the quantum theory has, the sillier it looks.
A. Einstein in 1912
By the end of the first decade of the twentieth century, three major quantum theoretical discoveries had been made. They concern the blackbody radiation law, the light-quantum postulate, and the quantum theory of the specific heat of solids. All three arose from statistical considerations. There are, however, striking differences in the time intervals between these theoretical advances and their respective experimental justification. Planck formulated his radiation law in an uncommonly short time after learning about experiments in the far infrared that complemented earlier results at higher frequencies. It was quite a different story with the light- quantum. Einstein's hypothesis was many years ahead of its decisive experimental tests. As we shall see next, the story is quite different again in the case of specific heats. Einstein's first paper on the subject [E1], submitted in November 1906, contains the qualitatively correct explanation of an anomaly that had been observed as early as 1840: the low value of the specific heat of diamond at room temperature. Einstein showed that this can be understood as a quantum effect. His paper contains one graph, the specific heat of diamond as a function of temperature, reproduced here below, which represents the first published graph in the history of the quantum theory of the solid state. It also represents one of only three instances I know of in which Einstein published a graph to compare theory with experiment (another example will be mentioned in Section 20b).
In order to recognize an anomaly, one needs a theory or a rule or at least a prejudice. As I just mentioned, peculiarities in specific heats were diagnosed more than half a century before Einstein explained them. It was also known well before 1906 that specific heats of gases exhibited even more curious properties. In what way was diamond considered so exceptional? And what about other substances? For a perspective on Einstein's contributions, it is necessary to sketch the answer to these questions. I therefore begin with a short account of specific heats in the nineteenth century.